Brush the mushrooms clean with a dry towel. Place mushrooms in a food processor in batches, about 1/4 at a time, and pulse several times to grind. You want them finely diced, but not mushy. (See notes.)
Use the Saute feature of your Instant Pot, use the Adjust button to set the heat to More (high). Heat about a tablespoon of water, then add the onion and a pinch of salt and saute for 5 minutes. Add the garlic and saute for 2 minutes. Add water a little at a time if things begin to stick.
Add the mushrooms and saute until browned and most of the liquid has evaporated, about 10-12 minutes.
Add the cumin, chili powder, fennel, cayenne pepper and cocoa powder. Stir to combine.
Deglaze (loosen and scrape up any brown bits) with the coffee. Add the smashed tomatoes and their liquid, beans, and water.
Turn off the Saute setting. Close the Instant Pot lid, and make sure the steam release handle is in the Sealing position. Cook on Manual (or Pressure Cook) mode for 30 minutes.
Allow the Instant Pot to do a Natural Release for 10 minutes. After 10 minutes, do a Quick Release--carefully move the steam release handle to the Venting position to release the additional steam until the float valve drops down. Press Cancel and open the lid.
The chili will thicken a bit as it rests. But if desired, you can thicken it more by sautéing a few minutes on medium heat. Add sea salt to taste and serve.
Shitake mushrooms can be expensive, but add a rich, earthy flavor. It's fine to use a smaller amount shitakes or substitute them completely with cremini or white button mushrooms. Just make sure you have about 1 1/2 pounds total.
Shitake mushrooms have a tough section on the end of their stem. I snip those off with kitchen shears.
To soak beans, cover them with about 2 inches of water and set them out on the counter. After 8-10 hours, drain and rinse them.
If some large pieces of mushrooms remain, don't keep pulsing. You want them finely ground but not mushy. Remove any large pieces and set them aside. Transfer the ground mushrooms from the food processor to a bowl. Then, add any large pieces back to the processor with the next batch and repeat until all of the mushrooms are finely ground.
Chopping whole tomatoes can make a mess! To avoid this, empty the whole can into a large bowl and break them up them with a potato masher, or place them in the food processor and process on low for about 15 seconds. I prefer to use whole tomatoes, as canned diced tomatoes contain a chemical (to keep them from dissolving), which alters the flavor. Also, I find there's no match for the flavor of San Marzanos.